Reproducible Documentation of Analysis Study 1

R Version

Code 
R.Version()
$platform
[1] "aarch64-apple-darwin20"

$arch
[1] "aarch64"

$os
[1] "darwin20"

$system
[1] "aarch64, darwin20"

$status
[1] ""

$major
[1] "4"

$minor
[1] "2.2"

$year
[1] "2022"

$month
[1] "10"

$day
[1] "31"

$`svn rev`
[1] "83211"

$language
[1] "R"

$version.string
[1] "R version 4.2.2 (2022-10-31)"

$nickname
[1] "Innocent and Trusting"

Import of the Data

The data was assessed with the formr survey framework (Arslan, Walther, and Tata 2020). The raw data was imported via the following code.

Please note that the results of the Bayesian analyses may slightly vary due to the estimation approach.

Code 
library(tidyverse)
library(ggforce)
library(lme4)
library(BFpack)
library(hrbrthemes)
library(patchwork)
library(brms)
library(viridis)
library(ggdist)
library(tidybayes)
library(here)
library(skimr)
load(here("data/teachers_study1_N40.RData"))

skim(study1)

set.seed(25051982)

Data Wrangling

Data Set 1

(without efficiency and accuracy transformed)

Code 
# wrangle information on the plot type, ES, ...
plot_info <- study1 %>%
    pivot_longer(2:195, names_to = "variables", values_to = "values", 
                 values_transform = as.character) %>%
    dplyr::filter(str_detect(variables, "plot")) %>% 
    # we only need the rows with info on plots
    tidyr::separate(col = values, into = c("type", "axis", "effsize"), 
                    # separate the info into three columns
                    sep = "_", remove = F) %>%
    dplyr::mutate(plot = variables,       # rename variables for later join
                  type = paste(type, axis, sep = "_")) %>%
    dplyr::select(-variables, -axis)

# wrangle answers to items on each page
item_values <- study1 %>%
    dplyr::select(-c(topic:itemo)) %>%
    pivot_longer(2:169, names_to = "variables", values_to = "values", 
                 values_transform = as.character) %>%
    dplyr::mutate(variables = case_when(      # recode variable names that have
        variables == "sensi_6" ~ "sensi_06",  # accidentally been labeled
        variables == "acccl_6" ~ "acccl_06",  # without zero
        variables == "accu3_6" ~ "accu3_06",
        variables == "accov_6" ~ "accov_06",
        variables == "diffi_6" ~ "diffi_06",
        variables == "infor_6" ~ "infor_06",
        variables == "value_6" ~ "value_06",
        TRUE ~ variables 
    )) %>%
    dplyr::mutate(plot = paste0("plotx_", str_sub(variables, -2, -1)), 
                  # create variable for later join
                  variables = str_sub(variables, 1, -4)) %>%    
    # rename variable names to get a data set 
    # with one line per participant per page
    pivot_wider(id_cols = c(session, plot), names_from = "variables", 
                values_from = "values")

# join the two data sets
study1_w <- full_join(plot_info, item_values, 
                               by = c("session", "plot")) %>% 
    # by participant and page (plot)
    dplyr::select(-values) %>%
    dplyr::mutate(rating_am = as.numeric(acccl), # some var need to be defined as
                  rating_u3 = as.numeric(accu3), # numeric again
                  rating_ov = as.numeric(accov),
                  diffi = as.numeric(diffi),
                  infor = as.numeric(infor),
                  value = as.numeric(value),
                  effsize = as.numeric(effsize),
                  effsize_am = case_when( 
                  # there is no negative Cliff's Delta, so we have to compute 
                  # two transformations
                      effsize > 0 ~   (((2*pnorm(effsize/2))-1)/pnorm(effsize/2)),
                  # transform the actual effect size Cohen's d to Cliff's Delta
                      effsize < 0 ~ (- (((2*pnorm(abs(effsize)/2))-1)/pnorm(abs(effsize)/2))) 
                  # transform the actual effect size Cohen's d to Cliff's Delta 
                  # and make it negative as in the item
                  ),
                  effsize_u3 = 1-pnorm(effsize), # reverse so that it fits the direction of the U3 item
                  # transform the actual effect size Cohen's d to Cohen's U3
                  effsize_ov = 2 * pnorm(-abs(effsize) / 2), 
                  # transform the actual effect size Cohen's d to overlap
                  # actual difference of rating relative to depicted effectsize 
                  diff_am = (rating_am - effsize_am)/2,
                  # actual difference of rating relative to depicted effectsize
                  diff_u3 = (rating_u3/100) - effsize_u3,
                  # actual difference of rating relative to depicted effectsize 
                  diff_ov = (rating_ov/100) - effsize_ov) %>%
    group_by(session) %>% 
    mutate(rating_ov_missconcept = median(rating_ov, na.rm = T) < 68.9,
           rating_u3_missconcept = median(rating_u3, na.rm = T) < 21.2) %>% 
    ungroup() %>% 
    mutate(rating_u3_filtered = ifelse(rating_u3_missconcept == T, NA, rating_u3),
           rating_ov_filtered = ifelse(rating_ov_missconcept == T, NA, rating_ov),
           diff_u3_filtered = (rating_u3_filtered/100) - effsize_u3,
           diff_ov_filtered = (rating_ov_filtered/100) - effsize_ov,
           sensi_binary = ifelse(is.na(sensi), # 1 if NOT "equal"
                                        NA,
                                        as.numeric(!grepl("equal", sensi))),
           sensi_ordinal = ordered(factor(substr(sensi, 55, 100)),
                                   levels = c("inferior",
                                              "equal",
                                              "superior")),
           sensi_binary_filtered = case_when(sensi_ordinal == "equal" ~ 0, 
                                             (sensi_ordinal == "inferior" & 
                                                  effsize < 0) | 
                                                  (sensi_ordinal == "superior" & 
                                                  effsize > 0) ~ as.numeric(NA),
                                             (sensi_ordinal == "inferior" & # was not there
                                                  effsize > 0) | 
                                                  (sensi_ordinal == "superior" & 
                                                  effsize < 0) ~ 1, 
                                             TRUE ~ as.numeric(NA)), # was 1
           sensi_correct = case_when(sensi_ordinal == "equal" ~ "judged equal", 
                                     (sensi_ordinal == "inferior" & 
                                                  effsize < 0) | 
                                                  (sensi_ordinal == "superior" & 
                                                  effsize > 0) ~ "wrong direction",
                                             (sensi_ordinal == "inferior" & # was not there
                                                  effsize > 0) | 
                                                  (sensi_ordinal == "superior" & 
                                                  effsize < 0) ~ "right direction", 
                                             TRUE ~ NA_character_),
           effsize_abs = abs(effsize))


Basic Information on data set

Code 
skim(study1_w)
Data summary
Name study1_w
Number of rows 960
Number of columns 31
_______________________
Column type frequency:
character 8
factor 1
logical 2
numeric 20
________________________
Group variables None

Variable type: character

skim_variable n_missing complete_rate min max empty n_unique whitespace
session 0 1.0 64 64 0 40 0
type 0 1.0 13 19 0 4 0
plot 0 1.0 8 8 0 24 0
sensi 480 0.5 59 62 0 3 0
acccl 480 0.5 1 4 0 11 0
accu3 480 0.5 1 3 0 48 0
accov 480 0.5 1 3 0 52 0
sensi_correct 480 0.5 12 15 0 3 0

Variable type: factor

skim_variable n_missing complete_rate ordered n_unique top_counts
sensi_ordinal 480 0.5 TRUE 3 sup: 177, inf: 159, equ: 144

Variable type: logical

skim_variable n_missing complete_rate mean count
rating_ov_missconcept 0 1 0.22 FAL: 744, TRU: 216
rating_u3_missconcept 0 1 0.55 TRU: 528, FAL: 432

Variable type: numeric

skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist
effsize 0 1.00 0.00 0.56 -0.80 -0.50 0.00 0.50 0.80 ▇▃▁▃▇
diffi 0 1.00 4.05 1.71 1.00 3.00 4.00 5.00 7.00 ▇▆▆▆▇
infor 0 1.00 4.11 1.45 1.00 3.00 4.00 5.00 7.00 ▅▅▇▇▅
value 0 1.00 4.13 1.49 1.00 3.00 4.00 5.00 7.00 ▅▃▆▇▅
rating_am 480 0.50 0.01 0.38 -1.00 -0.20 0.00 0.20 1.00 ▂▆▇▃▁
rating_u3 480 0.50 26.17 22.60 0.00 6.00 18.00 45.00 100.00 ▇▃▃▁▁
rating_ov 480 0.50 71.63 28.63 0.00 65.00 80.00 90.00 100.00 ▂▁▁▅▇
effsize_am 0 1.00 0.00 0.34 -0.47 -0.33 0.00 0.33 0.47 ▇▃▁▃▇
effsize_u3 0 1.00 0.50 0.21 0.21 0.31 0.50 0.69 0.79 ▇▃▁▃▇
effsize_ov 0 1.00 0.80 0.09 0.69 0.69 0.80 0.92 0.92 ▇▁▇▁▇
diff_am 480 0.50 0.01 0.18 -0.54 -0.06 0.00 0.07 0.64 ▁▂▇▂▁
diff_u3 480 0.50 -0.24 0.29 -0.79 -0.49 -0.21 -0.03 0.69 ▅▆▇▂▁
diff_ov 480 0.50 -0.09 0.29 -0.92 -0.12 0.01 0.10 0.31 ▂▁▁▇▅
rating_u3_filtered 744 0.22 43.06 17.90 0.00 30.00 45.00 55.00 80.00 ▂▃▇▇▂
rating_ov_filtered 588 0.39 82.60 16.81 0.00 80.00 85.00 90.00 100.00 ▁▁▁▅▇
diff_u3_filtered 744 0.22 -0.06 0.22 -0.79 -0.15 -0.03 0.06 0.54 ▁▂▇▅▁
diff_ov_filtered 588 0.39 0.02 0.17 -0.92 -0.02 0.05 0.10 0.31 ▁▁▁▇▅
sensi_binary 480 0.50 0.70 0.46 0.00 0.00 1.00 1.00 1.00 ▃▁▁▁▇
sensi_binary_filtered 507 0.47 0.68 0.47 0.00 0.00 1.00 1.00 1.00 ▃▁▁▁▇
effsize_abs 0 1.00 0.50 0.25 0.20 0.20 0.50 0.80 0.80 ▇▁▇▁▇



Data Set 2

(with efficiency and accuracy transformed)

Code 
# create a list of u3_misconceptualizers
u3_misconceptualizers <-
    study1_w %>% 
    filter(rating_u3_missconcept == T) %>% 
    pull(session) %>% 
    unique()

# create a list of ov_misconceptualizers
ov_misconceptualizers <-
    study1_w %>% 
    filter(rating_ov_missconcept == T) %>% 
    pull(session) %>% 
    unique()    

### wrangle time stamp data ####################################################
study1_w_timestamp <- 
    read_csv(here("data/teachers_study1_N40_detailed.csv")) %>% 
    # filter participants from study1_w only
    filter(session %in% study1_w$session) %>% 
    # we only need vars sensitivity or accuracy
    dplyr::filter(str_detect(item_name, "sensi|acccl|accu3|accov")) %>%  
    # create var with plot number
    mutate(plot = paste0("plotx_", str_sub(item_name, -2, -1)),
           # recode wrong item labelling
           plot = ifelse(plot == "plotx__6", "plotx_06", plot)) %>% 
    relocate(session, plot) %>% 
    # delete the page number in item name
    mutate(item_name = str_sub(item_name, 1, 5)) %>%  
    pivot_wider(id_cols = c(session, plot), names_from = item_name, 
                values_from = answered_relative) %>% 
    rowwise() %>%
    # what was the time of the first item to be clicked?
    mutate(effic = min(sensi, acccl, accu3, accov, na.rm=T)) %>%
    ungroup() %>% 
    dplyr::select(session, plot, effic, sensi, acccl, accu3, accov) %>% 
    left_join(., study1_w %>% 
                  select(session, plot, type), by=c("session", "plot")) %>% 
    # generate data set so that the six plots from the same type are ordered
    # one after the other (and not 1-24)
    group_by(session, type) %>% 
    arrange(plot) %>% 
    mutate(plotNrWithin = 1:n()) %>%
    ungroup() %>% 
    group_by(plotNrWithin, type) %>% 
    mutate(effic_10righttrunc = ifelse(effic > quantile(effic, .9), NA, effic),
           effic_05righttrunc = ifelse(effic > quantile(effic, .95), NA, effic),
           log_effic_05righttrunc =log(effic_05righttrunc),
           log_effic_10righttrunc = log(effic_10righttrunc),
           plotNrWithin0 = plotNrWithin -1,
           plotNrWithin_factor = as.factor(plotNrWithin)) %>% 
    ungroup()


Basic information on data set

Code 
skim(study1_w_timestamp)
Data summary
Name study1_w_timestamp
Number of rows 960
Number of columns 15
_______________________
Column type frequency:
character 3
factor 1
numeric 11
________________________
Group variables None

Variable type: character

skim_variable n_missing complete_rate min max empty n_unique whitespace
session 0 1 64 64 0 40 0
plot 0 1 8 8 0 24 0
type 0 1 13 19 0 4 0

Variable type: factor

skim_variable n_missing complete_rate ordered n_unique top_counts
plotNrWithin_factor 0 1 FALSE 6 1: 160, 2: 160, 3: 160, 4: 160

Variable type: numeric

skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist
effic 0 1.00 28817.81 67778.16 2419.00 9065.93 14866.60 26444.00 1342595.60 ▇▁▁▁▁
sensi 480 0.50 22664.69 53591.36 2419.00 7670.72 11408.65 20709.33 684967.00 ▇▁▁▁▁
acccl 557 0.42 33590.02 83104.51 3547.30 11650.00 18116.60 32103.65 1349401.70 ▇▁▁▁▁
accu3 480 0.50 61388.83 88359.00 5599.30 22174.12 39723.25 70041.55 1342595.60 ▇▁▁▁▁
accov 480 0.50 69364.58 90056.87 6901.30 26939.18 46882.25 79074.25 1344927.30 ▇▁▁▁▁
plotNrWithin 0 1.00 3.50 1.71 1.00 2.00 3.50 5.00 6.00 ▇▃▃▃▃
effic_10righttrunc 96 0.90 16914.40 11789.22 2419.00 8734.20 13402.60 21572.35 89854.90 ▇▂▁▁▁
effic_05righttrunc 48 0.95 19435.38 17815.29 2419.00 8910.87 14118.35 23782.15 168247.90 ▇▁▁▁▁
log_effic_05righttrunc 48 0.95 9.60 0.71 7.79 9.10 9.56 10.08 12.03 ▂▇▇▃▁
log_effic_10righttrunc 96 0.90 9.53 0.64 7.79 9.08 9.50 9.98 11.41 ▁▆▇▅▁
plotNrWithin0 0 1.00 2.50 1.71 0.00 1.00 2.50 4.00 5.00 ▇▃▃▃▃



Sample Description

Sociodemographics

Code 
# socio demographics 
sociodemographics <- read_delim("data/teachers_study1a.csv", delim = ";") %>%
    select(session, mcstu, texpe, mcsub) %>% 
    # filter(!is.na(mcstu & texpe)) %>%
    mutate(reply = session %in% c(study1_w$session)) %>%
    filter(!reply == "FALSE") %>%
    select(-reply) %>%
    mutate(mcstu = as.factor(mcstu),
    texpe = as.numeric(texpe),
    mcsub = as.factor(mcsub),
    subject_stem = grepl("1", mcsub),
    subject_languages = grepl("2", mcsub),
    subject_humanities_socialscience = grepl("3", mcsub),
    subject_asthetic = grepl("4", mcsub)) 

skim(sociodemographics)
Data summary
Name sociodemographics
Number of rows 40
Number of columns 8
_______________________
Column type frequency:
character 1
factor 2
logical 4
numeric 1
________________________
Group variables None

Variable type: character

skim_variable n_missing complete_rate min max empty n_unique whitespace
session 0 1 64 64 0 40 0

Variable type: factor

skim_variable n_missing complete_rate ordered n_unique top_counts
mcstu 0 1 FALSE 6 6: 15, 1: 9, 2: 7, 3: 6
mcsub 0 1 FALSE 10 1: 8, 3: 8, 2: 7, 1, : 3

Variable type: logical

skim_variable n_missing complete_rate mean count
subject_stem 0 1 0.48 FAL: 21, TRU: 19
subject_languages 0 1 0.45 FAL: 22, TRU: 18
subject_humanities_socialscience 0 1 0.50 FAL: 20, TRU: 20
subject_asthetic 0 1 0.15 FAL: 34, TRU: 6

Variable type: numeric

skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist
texpe 0 1 10.15 8.66 2 4 7 13.5 37.5 ▇▃▂▁▁
Code 
study1_w_demo <- full_join(study1_w, sociodemographics, by = "session") %>%
    mutate(schooltype_binary = ifelse(mcstu == 6, 1, 0)) # 6 = other

N = 15 participants checked “other” when asked which school type they teach at. This might be problematic as we cannot guarantee that these participants are actual school teachers. Hence, we decided to explore differences between those participants who indicated to work at a a specific school type and those that indicated “other” (see section Are there Differences Between Particpants That Indicated a Specific School Type and Those That Indicated “other”?).

Descriptives of the Dependent Variables

Descriptives of Accuracy and Perceived Variables Across all Visualization Types

Show the code 
skim(study1_w %>%
         select(diffi, infor, value, rating_u3, rating_ov, rating_am, diff_u3,
                diff_ov, diff_am))
Data summary
Name %>%(…)
Number of rows 960
Number of columns 9
_______________________
Column type frequency:
numeric 9
________________________
Group variables None

Variable type: numeric

skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist
diffi 0 1.0 4.05 1.71 1.00 3.00 4.00 5.00 7.00 ▇▆▆▆▇
infor 0 1.0 4.11 1.45 1.00 3.00 4.00 5.00 7.00 ▅▅▇▇▅
value 0 1.0 4.13 1.49 1.00 3.00 4.00 5.00 7.00 ▅▃▆▇▅
rating_u3 480 0.5 26.17 22.60 0.00 6.00 18.00 45.00 100.00 ▇▃▃▁▁
rating_ov 480 0.5 71.63 28.63 0.00 65.00 80.00 90.00 100.00 ▂▁▁▅▇
rating_am 480 0.5 0.01 0.38 -1.00 -0.20 0.00 0.20 1.00 ▂▆▇▃▁
diff_u3 480 0.5 -0.24 0.29 -0.79 -0.49 -0.21 -0.03 0.69 ▅▆▇▂▁
diff_ov 480 0.5 -0.09 0.29 -0.92 -0.12 0.01 0.10 0.31 ▂▁▁▇▅
diff_am 480 0.5 0.01 0.18 -0.54 -0.06 0.00 0.07 0.64 ▁▂▇▂▁

Descriptives of Accuracy and Perceived Variables Grouped by Visualization Types

Show the code 
skim(study1_w %>%
         select(diffi, infor,value,rating_u3, rating_ov, rating_am, diff_u3, diff_ov, diff_am,  session, type, plot) %>%
    gather(var, value, diffi, infor,value,rating_u3, rating_ov, rating_am, diff_u3, diff_ov, diff_am)%>%
    mutate(variable = paste(var, type, sep = "_"))%>%
    select(-type, -var)%>%
    group_by(session, plot) %>%
    spread(variable, value) %>%
    ungroup())
Data summary
Name %>%(…)
Number of rows 960
Number of columns 38
_______________________
Column type frequency:
character 2
numeric 36
________________________
Group variables None

Variable type: character

skim_variable n_missing complete_rate min max empty n_unique whitespace
session 0 1 64 64 0 40 0
plot 0 1 8 8 0 24 0

Variable type: numeric

skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist
diff_am_gardneraltman_xaxis 843 0.12 0.00 0.20 -0.54 -0.07 0.03 0.07 0.54 ▁▂▇▃▁
diff_am_halfeye_xaxis 834 0.13 -0.01 0.15 -0.44 -0.07 -0.03 0.06 0.54 ▁▅▇▁▁
diff_am_halfeye_yaxis 842 0.12 0.02 0.17 -0.54 -0.06 0.03 0.14 0.54 ▁▂▇▃▁
diff_am_raincloud_yaxis 841 0.12 0.01 0.18 -0.37 -0.07 -0.03 0.13 0.64 ▃▇▇▂▁
diff_ov_gardneraltman_xaxis 843 0.12 -0.11 0.31 -0.92 -0.17 0.00 0.10 0.26 ▂▁▁▅▇
diff_ov_halfeye_xaxis 834 0.13 -0.07 0.28 -0.92 -0.11 0.03 0.10 0.31 ▁▁▁▇▅
diff_ov_halfeye_yaxis 842 0.12 -0.11 0.31 -0.92 -0.10 0.00 0.08 0.21 ▂▁▁▃▇
diff_ov_raincloud_yaxis 841 0.12 -0.07 0.26 -0.92 -0.10 0.01 0.09 0.31 ▁▁▁▇▅
diff_u3_gardneraltman_xaxis 843 0.12 -0.22 0.29 -0.79 -0.44 -0.19 -0.03 0.69 ▃▅▇▂▁
diff_u3_halfeye_xaxis 834 0.13 -0.23 0.28 -0.79 -0.47 -0.19 -0.01 0.39 ▃▆▅▇▁
diff_u3_halfeye_yaxis 842 0.12 -0.24 0.30 -0.79 -0.54 -0.21 -0.02 0.54 ▇▅▇▃▁
diff_u3_raincloud_yaxis 841 0.12 -0.25 0.28 -0.79 -0.50 -0.21 -0.03 0.39 ▆▆▇▇▂
diffi_gardneraltman_xaxis 720 0.25 3.59 1.87 1.00 2.00 3.00 5.00 7.00 ▇▅▃▃▅
diffi_halfeye_xaxis 720 0.25 4.23 1.54 1.00 3.00 4.00 6.00 7.00 ▅▇▆▆▇
diffi_halfeye_yaxis 720 0.25 4.55 1.58 1.00 3.00 5.00 6.00 7.00 ▃▃▃▆▇
diffi_raincloud_yaxis 720 0.25 3.83 1.68 1.00 2.75 4.00 5.00 7.00 ▇▆▆▅▆
infor_gardneraltman_xaxis 720 0.25 3.80 1.57 1.00 3.00 4.00 5.00 7.00 ▆▅▆▇▃
infor_halfeye_xaxis 720 0.25 4.19 1.34 1.00 3.00 4.00 5.00 7.00 ▃▆▇▇▅
infor_halfeye_yaxis 720 0.25 4.40 1.35 1.00 3.00 4.50 5.00 7.00 ▂▅▇▇▆
infor_raincloud_yaxis 720 0.25 4.04 1.48 1.00 3.00 4.00 5.00 7.00 ▅▃▇▆▅
rating_am_gardneraltman_xaxis 843 0.12 0.03 0.40 -1.00 -0.20 0.00 0.20 1.00 ▂▅▇▃▁
rating_am_halfeye_xaxis 834 0.13 0.00 0.36 -1.00 -0.20 0.00 0.20 1.00 ▁▇▇▂▁
rating_am_halfeye_yaxis 842 0.12 0.01 0.40 -1.00 -0.20 0.00 0.20 1.00 ▂▇▇▃▁
rating_am_raincloud_yaxis 841 0.12 0.03 0.38 -1.00 -0.20 0.00 0.20 0.80 ▁▃▇▆▂
rating_ov_gardneraltman_xaxis 843 0.12 68.63 30.39 0.00 60.00 80.00 90.00 100.00 ▂▁▂▅▇
rating_ov_halfeye_xaxis 834 0.13 74.73 26.46 0.00 70.00 85.00 90.00 100.00 ▂▁▁▃▇
rating_ov_halfeye_yaxis 842 0.12 70.08 30.92 0.00 66.25 80.00 90.00 100.00 ▂▁▁▅▇
rating_ov_raincloud_yaxis 841 0.12 72.83 26.57 0.00 67.50 80.00 90.00 100.00 ▂▁▁▅▇
rating_u3_gardneraltman_xaxis 843 0.12 26.56 21.61 0.00 7.00 22.00 45.00 100.00 ▇▃▅▁▁
rating_u3_halfeye_xaxis 834 0.13 26.73 23.01 0.00 5.25 20.00 48.75 80.00 ▇▂▂▃▁
rating_u3_halfeye_yaxis 842 0.12 27.08 23.33 0.00 7.00 15.00 50.00 75.00 ▇▁▂▃▁
rating_u3_raincloud_yaxis 841 0.12 24.28 22.54 0.00 5.50 15.00 40.00 100.00 ▇▃▂▁▁
value_gardneraltman_xaxis 720 0.25 3.80 1.51 1.00 3.00 4.00 5.00 7.00 ▆▅▇▇▃
value_halfeye_xaxis 720 0.25 4.31 1.40 1.00 3.75 5.00 5.00 7.00 ▃▃▆▇▅
value_halfeye_yaxis 720 0.25 4.38 1.39 1.00 4.00 5.00 5.00 7.00 ▂▂▅▇▃
value_raincloud_yaxis 720 0.25 4.03 1.58 1.00 3.00 4.00 5.00 7.00 ▆▃▆▇▅

Descriptives of Efficiency Across Visualization Types

Show the code 
skim(study1_w_timestamp %>%
    select(effic, session))
Data summary
Name study1_w_timestamp %>% se…
Number of rows 960
Number of columns 2
_______________________
Column type frequency:
character 1
numeric 1
________________________
Group variables None

Variable type: character

skim_variable n_missing complete_rate min max empty n_unique whitespace
session 0 1 64 64 0 40 0

Variable type: numeric

skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist
effic 0 1 28817.81 67778.16 2419 9065.93 14866.6 26444 1342596 ▇▁▁▁▁

Descriptives of Efficiency Grouped by Visualization Types

Show the code 
skim(study1_w_timestamp %>%
    select(effic, session, type, plot) %>%
    gather(var, value, effic)%>%
    mutate(variable = paste(var, type, sep = "_"))%>%
    select(-type, -var)%>%
    group_by(session, plot) %>%
    spread(variable, value) %>%
    ungroup())
Data summary
Name %>%(…)
Number of rows 960
Number of columns 6
_______________________
Column type frequency:
character 2
numeric 4
________________________
Group variables None

Variable type: character

skim_variable n_missing complete_rate min max empty n_unique whitespace
session 0 1 64 64 0 40 0
plot 0 1 8 8 0 24 0

Variable type: numeric

skim_variable n_missing complete_rate mean sd p0 p25 p50 p75 p100 hist
effic_gardneraltman_xaxis 720 0.25 35739.25 99037.01 3547.3 10743.50 17592.75 32584.00 1342595.6 ▇▁▁▁▁
effic_halfeye_xaxis 720 0.25 27179.72 62047.66 2897.0 8788.35 13740.70 23012.73 684967.0 ▇▁▁▁▁
effic_halfeye_yaxis 720 0.25 23954.41 44387.89 2419.0 8960.30 13016.15 23628.10 466834.3 ▇▁▁▁▁
effic_raincloud_yaxis 720 0.25 28397.86 52248.67 2769.0 8910.65 14126.85 25963.05 598871.6 ▇▁▁▁▁



Are there Differences Between Particpants That Indicated a Specific School Type and Those That Indicated “other”?

Graphical Overview

Code 
study1_w_demo %>% 
    ggplot(., aes(effsize, rating_am, color = as.factor(schooltype_binary))) +
    geom_jitter() +
    stat_smooth() +
    ylab("Abstract metric") +
    xlab("Plotted effect size") +
    labs(color = "Schooltype") +
    theme_modern_rc()

Code 
study1_w_demo%>% 
    ggplot(., aes(effsize_u3, rating_u3, color = as.factor(schooltype_binary))) +
    geom_jitter() +
    stat_smooth() +
    ylab("Cohen's U3 metric") +
    xlab("Plotted effect size") +
    labs(color = "Schooltype") +
    theme_modern_rc()

Code 
study1_w_demo %>% 
    ggplot(., aes(effsize_abs, rating_ov, color = as.factor(schooltype_binary))) +
    geom_jitter() +
    stat_smooth(method = "lm") +
    ylab("Overlap metric") +
    xlab("Plotted effect size") +
    labs(color = "Schooltype") +
    theme_modern_rc()

Code 
study1_w_demo %>% 
ggplot(., aes(as.factor(schooltype_binary), infor)) +
    geom_jitter()+
    stat_summary(fun.data = mean_sdl,
                 fun.args = list(mult =1),
                 color = "white") +
    ylab("Perceived Informativity") +
    xlab("School Type 1") +
    theme_modern_rc()

Code 
study1_w_demo %>%
ggplot(., aes(as.factor(schooltype_binary), diffi)) +
    geom_jitter()+
    stat_summary(fun.data = mean_sdl,
                 fun.args = list(mult =1),
                 color = "white") +
    ylab("Perceived Difficulty") +
    xlab("School Type") +
    theme_modern_rc()

Code 
study1_w_demo %>%
ggplot(., aes(as.factor(schooltype_binary), value)) +
    geom_jitter()+
    stat_summary(fun.data = mean_sdl,
                 fun.args = list(mult =1),
                 color = "white") +
    ylab("Perceived Value") +
    xlab("School Type 1=others") +
    theme_modern_rc()

Compute Kendall’s \(\tau\) for rating_am, rating_u3 and rating_ov

Show the code 
## accuracy U3 
### overall 
study1_w_demo %>% 
    do(tau_u3 = unlist(cor(.$effsize_u3, .$rating_u3, method = "kendall", 
                           use = "pairwise.complete"))) %>% 
    unnest(tau_u3)
# A tibble: 1 × 1
  tau_u3
   <dbl>
1 0.0837
Show the code 
### grouped by plot type 
study1_w_demo %>% 
    group_by(type) %>% 
    do(tau_u3 = unlist(cor(.$effsize_u3, .$rating_u3, method = "kendall", 
                           use = "pairwise.complete"))) %>% 
    unnest(tau_u3)
# A tibble: 4 × 2
  type                tau_u3
  <chr>                <dbl>
1 gardneraltman_xaxis 0.0334
2 halfeye_xaxis       0.143 
3 halfeye_yaxis       0.0423
4 raincloud_yaxis     0.118
Show the code 
### grouped by school type
study1_w_demo %>% 
    group_by(schooltype_binary) %>% 
    do(tau_u3a = unlist(cor(.$effsize_u3, .$rating_u3, method = "kendall", 
                           use = "pairwise.complete"))) %>% 
    unnest(tau_u3a)
# A tibble: 2 × 2
  schooltype_binary tau_u3a
              <dbl>   <dbl>
1                 0  0.0649
2                 1  0.122
Show the code 
### grouped by school type and plot type
study1_w_demo %>% 
    group_by(schooltype_binary, type) %>% 
    do(tau_u3 = unlist(cor(.$effsize_u3, .$rating_u3, method = "kendall", 
                           use = "pairwise.complete"))) %>% 
    unnest(tau_u3)
# A tibble: 8 × 3
  schooltype_binary type                 tau_u3
              <dbl> <chr>                 <dbl>
1                 0 gardneraltman_xaxis  0.0490
2                 0 halfeye_xaxis        0.123 
3                 0 halfeye_yaxis        0.0497
4                 0 raincloud_yaxis      0.0505
5                 1 gardneraltman_xaxis -0.0225
6                 1 halfeye_xaxis        0.175 
7                 1 halfeye_yaxis        0.0566
8                 1 raincloud_yaxis      0.234
Show the code 
## overlap 

### overall 
study1_w_demo %>% 
    do(tau_ov = unlist(cor(.$effsize_abs, .$rating_ov, method = "kendall", 
                           use = "pairwise.complete"))) %>% 
    unnest(tau_ov)
# A tibble: 1 × 1
  tau_ov
   <dbl>
1 -0.276
Show the code 
### grouped by plot type 
study1_w_demo %>% 
    group_by(type) %>% 
    do(tau_ov = unlist(cor(.$effsize_abs, .$rating_ov, method = "kendall", 
                           use = "pairwise.complete"))) %>% 
    unnest(tau_ov)
# A tibble: 4 × 2
  type                tau_ov
  <chr>                <dbl>
1 gardneraltman_xaxis -0.188
2 halfeye_xaxis       -0.228
3 halfeye_yaxis       -0.326
4 raincloud_yaxis     -0.348
Show the code 
### grouped by school type
study1_w_demo %>% 
    group_by(schooltype_binary) %>% 
    do(tau_ov = unlist(cor(.$effsize_abs, .$rating_ov, method = "kendall", 
                           use = "pairwise.complete"))) %>% 
    unnest(tau_ov)
# A tibble: 2 × 2
  schooltype_binary tau_ov
              <dbl>  <dbl>
1                 0 -0.233
2                 1 -0.345
Show the code 
### grouped by school type and plot type 
study1_w_demo %>% 
    group_by(schooltype_binary, type) %>% 
    do(tau_ov = unlist(cor(.$effsize_abs, .$rating_ov, method = "kendall", 
                           use = "pairwise.complete"))) %>% 
    unnest(tau_ov)
# A tibble: 8 × 3
  schooltype_binary type                tau_ov
              <dbl> <chr>                <dbl>
1                 0 gardneraltman_xaxis -0.201
2                 0 halfeye_xaxis       -0.105
3                 0 halfeye_yaxis       -0.195
4                 0 raincloud_yaxis     -0.410
5                 1 gardneraltman_xaxis -0.155
6                 1 halfeye_xaxis       -0.434
7                 1 halfeye_yaxis       -0.541
8                 1 raincloud_yaxis     -0.248
Show the code 
## Abstract Metric

### overall
study1_w_demo %>% 
    do(tau_am = unlist(cor(.$effsize, .$rating_am, method = "kendall", 
                           use = "pairwise.complete"))) %>% 
    unnest(tau_am)
# A tibble: 1 × 1
  tau_am
   <dbl>
1  0.449
Show the code 
### grouped by plot type
study1_w_demo %>% 
    group_by(type) %>% 
    do(tau_am = unlist(cor(.$effsize, .$rating_am, method = "kendall", 
                           use = "pairwise.complete"))) %>% 
    unnest(tau_am)
# A tibble: 4 × 2
  type                tau_am
  <chr>                <dbl>
1 gardneraltman_xaxis  0.373
2 halfeye_xaxis        0.548
3 halfeye_yaxis        0.484
4 raincloud_yaxis      0.415
Show the code 
### grouped by school type
study1_w_demo %>% 
    group_by(schooltype_binary) %>% 
    do(tau_am = unlist(cor(.$effsize, .$rating_am, method = "kendall", 
                           use = "pairwise.complete"))) %>% 
    unnest(tau_am)
# A tibble: 2 × 2
  schooltype_binary tau_am
              <dbl>  <dbl>
1                 0  0.373
2                 1  0.592
Show the code 
### grouped by school type and plot type
study1_w_demo %>% 
    group_by(schooltype_binary, type) %>% 
    do(tau_am = unlist(cor(.$effsize, .$rating_am, method = "kendall", 
                           use = "pairwise.complete"))) %>% 
    unnest(tau_am)
# A tibble: 8 × 3
  schooltype_binary type                tau_am
              <dbl> <chr>                <dbl>
1                 0 gardneraltman_xaxis  0.379
2                 0 halfeye_xaxis        0.442
3                 0 halfeye_yaxis        0.421
4                 0 raincloud_yaxis      0.280
5                 1 gardneraltman_xaxis  0.371
6                 1 halfeye_xaxis        0.699
7                 1 halfeye_yaxis        0.590
8                 1 raincloud_yaxis      0.701
Show the code 
study1_w_demo_vda <- study1_w_demo %>%
    select(session, plot, rating_ov, rating_am, rating_u3, schooltype_binary) %>%
    pivot_longer(rating_ov:rating_u3, names_to = "variables", 
                 values_to = "values") %>%
    mutate(var = paste(variables, schooltype_binary, sep = "_")) %>%
    select(-variables, values) %>%
    group_by(session, plot) %>%
    pivot_wider(names_from = "var", values_from = "values")

The results do not substantially differ between the two groups. Hence, we will include the participants indicated “other” school types in the following analyses.

Accuracy: Misconceptions

Distribution of the Accuracy Variables

Code 
study1_w %>% 
    select(rating_am, rating_u3, rating_ov) %>% 
    pivot_longer(
        c(rating_am, rating_u3, rating_ov),
        names_to = "dependent_variable", 
        values_to = "rated_effectsize"
        ) %>% 
    ggplot(., aes(rated_effectsize)) +
    geom_histogram() +
    xlab("Rated effect size") +
    facet_wrap(~dependent_variable, scales = "free_x", 
                labeller = as_labeller(c("rating_am" = "Abstract metric",
                                         "rating_ov" = "Overlap metric",
                                         "rating_u3" = "Cohen's U3 metric"))) +
    theme_modern_rc() +
    theme(strip.text = element_text(color = "white"))

Somewhat disturbing is the first mode in rating_ov. Maybe some users confused overlap and non-overlap? Another artifact seems to be the first mode in rating_u3.

Are there Constant Misconceptions per Persons?

Code 
ggplot(study1_w %>% 
    select(rating_am, rating_u3, rating_ov, effsize, effsize_am, session) %>% 
    pivot_longer(
        c(rating_am, rating_u3, rating_ov),
        names_to = "operationalization", 
        values_to = "judged_effectsize"
        ),
    aes(judged_effectsize, as.numeric(as.factor(session)),
        color = session)
        ) +
    geom_jitter(height = 0) +
    xlab("Rated effect size") +
    ylab("Participant ID") +
    facet_wrap(~ operationalization, scales = "free_x", 
                labeller = as_labeller(c("rating_am" = "Abstract metric",
                                         "rating_ov" = "Overlap metric",
                                         "rating_u3" = "Cohen's U3 metric"))) +
    theme_modern_rc() +
    theme(legend.position = "none",
          strip.text = element_text(color = "white"))

Association of Ratings and Actual Effect Size

Code 
study1_w %>% 
    ggplot(., aes(effsize, rating_am)) +
    geom_jitter() +
    stat_smooth() +
    ylab("Abstract metric") +
    xlab("Plotted effect size") +
    theme_modern_rc()

Code 
study1_w %>% 
    ggplot(., aes(effsize_u3, rating_u3, color = rating_u3_missconcept)) +
    geom_jitter() +
    stat_smooth() +
    ylab("Cohen's U3 metric") +
    xlab("Plotted effect size (transformed to U3)") +
    labs(color = "Misconcept") +
    theme_modern_rc()

Code 
study1_w %>% 
    ggplot(., aes(effsize_abs, rating_ov, color = rating_ov_missconcept)) +
    geom_jitter() +
    stat_smooth(method = "lm") +
    ylab("Overlap metric") +
    xlab("Plotted effect size") +
    labs(color = "Misconcept") +
    theme_modern_rc()

The correlations underpin the interpretation of the misconceptions. Therefore, we will look at the intercorrelations of the dependent variables.

Compute Kendall’s \(\tau\) for rating_am, rating_u3 and rating_ov

Show the code 
study1_w %>% 
    group_by(type) %>% 
    do(tau_am = unlist(cor(.$effsize, .$rating_am, method = "kendall", 
                           use = "pairwise.complete"))) %>% 
    unnest(tau_am)
# A tibble: 4 × 2
  type                tau_am
  <chr>                <dbl>
1 gardneraltman_xaxis  0.373
2 halfeye_xaxis        0.548
3 halfeye_yaxis        0.484
4 raincloud_yaxis      0.415
Show the code 
study1_w %>% 
    group_by(rating_ov_missconcept, type) %>% 
    do(tau_ov = unlist(cor(.$effsize_abs, .$rating_ov, method = "kendall", 
                           use = "pairwise.complete"))) %>% 
    unnest(tau_ov)
# A tibble: 8 × 3
  rating_ov_missconcept type                 tau_ov
  <lgl>                 <chr>                 <dbl>
1 FALSE                 gardneraltman_xaxis -0.355 
2 FALSE                 halfeye_xaxis       -0.384 
3 FALSE                 halfeye_yaxis       -0.478 
4 FALSE                 raincloud_yaxis     -0.523 
5 TRUE                  gardneraltman_xaxis  0.0236
6 TRUE                  halfeye_xaxis        0.119 
7 TRUE                  halfeye_yaxis        0.0205
8 TRUE                  raincloud_yaxis     -0.220
Show the code 
study1_w %>% 
    group_by(rating_u3_missconcept, type) %>% 
    do(tau_u3 = cor(.$effsize_u3, .$rating_u3, method = "kendall", 
                           use = "pairwise.complete")) %>% 
    unnest(tau_u3)
# A tibble: 8 × 3
  rating_u3_missconcept type                 tau_u3
  <lgl>                 <chr>                 <dbl>
1 FALSE                 gardneraltman_xaxis  0.298 
2 FALSE                 halfeye_xaxis        0.471 
3 FALSE                 halfeye_yaxis        0.263 
4 FALSE                 raincloud_yaxis      0.321 
5 TRUE                  gardneraltman_xaxis -0.119 
6 TRUE                  halfeye_xaxis        0.153 
7 TRUE                  halfeye_yaxis        0.108 
8 TRUE                  raincloud_yaxis      0.0971

Associations of the Dependent Variables

Code 
ggplot(study1_w, 
       aes(rating_am, rating_u3)) +
    geom_jitter() +
    xlab("Abstract metric") +
    ylab("Cohen's U3 metric") +
    theme_modern_rc() +
ggplot(study1_w, 
       aes(rating_am, rating_ov)) +
    geom_jitter() +
    xlab("Abstract metric") +
    ylab("Overlap metric") +
    theme_modern_rc() +
ggplot(study1_w, 
       aes(rating_ov, rating_u3)) +
    geom_jitter() +
    xlab("Overlap metric") +
    ylab("Cohen's U3 metric") +
    theme_modern_rc()

Global Under- or Overestimation

Code 
study1_w %>% 
    select(diff_am, diff_u3_filtered, diff_ov_filtered, session, type) %>% 
    gather(dependent_variable, difference_to_true_effsize, 
           diff_am, diff_u3_filtered, diff_ov_filtered) %>% 
    ggplot(., aes(type, difference_to_true_effsize)) +
    geom_boxplot(alpha = .3) +
    facet_wrap(~dependent_variable, scales = "free_y", 
                labeller = as_labeller(c("diff_am" = "Abstract metric",
                                         "diff_ov_filtered" = "Overlap metric (filtered)",
                                         "diff_u3_filtered" = "Cohen's U3 metric (filtered)"))) +
    geom_jitter(aes(color = type)) +
    ylab("Difference to true effect size") +
    xlab("Accuracy item") +
    labs(color = "Accuracy item") +
    theme_modern_rc() +
    theme(strip.text = element_text(color = "white"),
          axis.text.x = element_blank())

Research Question 1

Accuracy Abstract Metric

We generally compare

  1. a model (mod0) with intercept only
  2. a model (mod1) with intercept + plotted effect size (control variable)
  3. a model (mod2) with intercept + plotted effect size + visualization type

Random Intercept Models With and Without Visualization Type

Code 
# Difference variable 
mod0_diff_am <- brm(diff_am ~ + (1|session), 
                          data = study1_w,
                          iter = 20000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4)
mod1_diff_am <- brm(diff_am ~ effsize + (1|session), 
                          data = study1_w,
                          iter = 20000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4)
mod2_diff_am <- brm(diff_am ~ type + effsize + (1|session), 
                          data = study1_w,
                          iter = 10000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4
                          )
Code 
bayes_factor(mod1_diff_am, mod0_diff_am)
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Estimated Bayes factor in favor of mod1_diff_am over mod0_diff_am: 5525908941730420.00000
Code 
bayes_factor(mod2_diff_am, mod1_diff_am)
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Estimated Bayes factor in favor of mod2_diff_am over mod1_diff_am: 0.00015

Accuracy Cohen’s U3

We generally compare

  1. a model (mod0) with intercept only
  2. a model (mod1) with intercept + plotted effect size (control variable)
  3. a model (mod2) with intercept + plotted effect size + visualization type

Random Intercept Models With and Without Visualization Type

Code 
# Difference Variable 
mod0_diff_u3 <- brm(diff_u3 ~ + (1|session), 
                          data = study1_w%>% 
                              filter(rating_u3_missconcept == F),
                          iter = 10000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4
                          )

mod1_diff_u3 <- brm(diff_u3 ~ effsize_u3 + (1|session), 
                          data = study1_w%>% 
                              filter(rating_u3_missconcept == F),
                          iter = 10000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4
                          )

mod2_diff_u3 <- brm(diff_u3 ~ type + effsize_u3 + (1|session), 
                       data = study1_w %>% 
                           filter(rating_u3_missconcept == F),
                       iter = 10000,
                       save_pars = save_pars(all = TRUE),
                       cores = 4
                       )
Code 
bayes_factor(mod1_diff_u3, mod0_diff_u3)
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Estimated Bayes factor in favor of mod1_diff_u3 over mod0_diff_u3: 23494610594564530654305845248.00000
Code 
bayes_factor(mod2_diff_u3, mod1_diff_u3)
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Estimated Bayes factor in favor of mod2_diff_u3 over mod1_diff_u3: 0.00236

Accuracy overlap

We generally compare

  1. a model (mod0) with intercept only
  2. a model (mod1) with intercept + plotted effect size (control variable)
  3. a model (mod2) with intercept + plotted effect size + visualization type

Random Intercept Models With and Without Visualization Type

Code 
# Difference Variable
mod0_diff_ov <- brm(diff_ov ~ + (1|session), 
                          data = study1_w%>% 
                              filter(rating_ov_missconcept == F),
                          iter = 10000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4
                          )

mod1_diff_ov <- brm(diff_u3 ~ effsize_abs + (1|session), 
                          data = study1_w%>% 
                              filter(rating_u3_missconcept == F),
                          iter = 10000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4
                          )

mod2_diff_ov <- brm(diff_ov ~ type + effsize_abs + (1|session), 
                          data = study1_w %>% 
                              filter(rating_ov_missconcept == F),
                          iter = 10000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4
                          )
Code 
bayes_factor(mod1_diff_ov, mod0_diff_ov)
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Estimated Bayes factor in favor of mod1_diff_ov over mod0_diff_ov: 0.00000
Code 
bayes_factor(mod2_diff_ov, mod1_diff_ov)
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 6
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Estimated Bayes factor in favor of mod2_diff_ov over mod1_diff_ov: 4220238954760306197437326996142246058244242982043648.00000

Perceived Difficulty

Graphical Overview

Code 
study1_w %>% 
    ggplot(aes(type, diffi)) +
    geom_jitter() +
    stat_summary(fun.data = mean_sdl,
                 fun.args = list(mult = 1),
                 color = "white") +
    theme_modern_rc() +
    labs(title = "Difficulty",
         subtitle = "per Plot Type",
         caption = "Means ± 1*SD")

Random Intercept Models With and Without Visualization Type

We generally compare

  1. a model (mod0) with intercept only
  2. a model (mod1) with intercept + plotted effect size (control variable)
  3. a model (mod2) with intercept + plotted effect size + visualization type
Code 
# Perceived Difficulty
mod0_diffi <- brm(diffi ~ + (1|session), 
                          data = study1_w,
                          iter = 10000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4
                          )
mod1_diffi <- brm(diffi ~ effsize + (1|session), 
                          data = study1_w,
                          iter = 10000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4
                          )
mod2_diffi <- brm(diffi ~ type + effsize + (1|session), 
                          data = study1_w,
                          iter = 10000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4
                          )
Code 
bayes_factor(mod1_diffi, mod0_diffi)
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 6
Estimated Bayes factor in favor of mod1_diffi over mod0_diffi: 0.39638
Code 
bayes_factor(mod2_diffi, mod1_diffi)
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Estimated Bayes factor in favor of mod2_diffi over mod1_diffi: 4940787009100204.00000

Perceived Informativity

Graphical Overview

Code 
study1_w %>% 
    ggplot(aes(type, infor)) +
    geom_jitter() +
    stat_summary(fun.data = mean_sdl,
                 fun.args = list(mult = 1),
                 color = "white") +
    theme_modern_rc() +
    labs(title = "Informativity",
         subtitle = "per Plot Type",
         caption = "Means ± 1*SD")

Random Intercept Models With and Without Visualization Type

We generally compare

  1. a model (mod0) with intercept only
  2. a model (mod1) with intercept + plotted effect size (control variable)
  3. a model (mod2) with intercept + plotted effect size + visualization type
Code 
# Perceived Informativity
mod0_infor <- brm(infor ~ + (1|session), 
                          data = study1_w,
                          iter = 10000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4
                          )
mod1_infor <- brm(infor ~ effsize + (1|session), 
                          data = study1_w,
                          iter = 10000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4
                          )
mod2_infor <- brm(infor ~ type + effsize + (1|session), 
                          data = study1_w,
                          iter = 10000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4
                          )
Code 
bayes_factor(mod1_infor, mod0_infor)
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Estimated Bayes factor in favor of mod1_infor over mod0_infor: 0.25657
Code 
bayes_factor(mod2_infor, mod1_infor)
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Estimated Bayes factor in favor of mod2_infor over mod1_infor: 757517.30475

Perceived Value

Graphical Overview

Code 
study1_w %>% 
    ggplot(aes(type, value)) +
    geom_jitter() +
    stat_summary(fun.data = mean_sdl,
                 fun.args = list(mult = 1),
                 color = "white") +
    theme_modern_rc() +
    labs(title = "Perceived Value",
         subtitle = "per Plot Type",
         caption = "Means ± 1*SD")

Random Intercept Models With and Without Visualization Type

We generally compare

  1. a model (mod0) with intercept only
  2. a model (mod1) with intercept + plotted effect size (control variable)
  3. a model (mod2) with intercept + plotted effect size + visualization type
Code 
# Perceived Value 
mod0_value <- brm(value ~ + (1|session), 
                          data = study1_w,
                          iter = 10000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4
                          )
mod1_value <- brm(value ~ effsize + (1|session), 
                          data = study1_w,
                          iter = 10000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4
                          )
mod2_value <- brm(value ~ type + effsize + (1|session), 
                          data = study1_w,
                          iter = 10000,
                          save_pars = save_pars(all = TRUE),
                          cores = 4
                          )
Code 
bayes_factor(mod1_value, mod0_value)
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Estimated Bayes factor in favor of mod1_value over mod0_value: 0.21152
Code 
bayes_factor(mod2_value, mod1_value)
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 6
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Estimated Bayes factor in favor of mod2_value over mod1_value: 85840039.67506

Table of All Random Intercept Models

Code 
sjPlot::tab_model(
    mod0_diff_am, mod0_diff_u3, mod0_diff_ov,
    mod0_diffi, mod0_infor, mod0_value,
    mod1_diff_am, mod1_diff_u3, mod1_diff_ov,
    mod1_diffi, mod1_infor, mod1_value,
    mod2_diff_am, mod2_diff_u3, mod2_diff_ov,
    mod2_diffi, mod2_infor, mod2_value
    )
  diff_am diff_u3 diff_ov diffi infor value diff_am diff_u3 diff_u3 diffi infor value diff_am diff_u3 diff_ov diffi infor value
Predictors Estimates CI (95%) Estimates CI (95%) Estimates CI (95%) Estimates CI (95%) Estimates CI (95%) Estimates CI (95%) Estimates CI (95%) Estimates CI (95%) Estimates CI (95%) Estimates CI (95%) Estimates CI (95%) Estimates CI (95%) Estimates CI (95%) Estimates CI (95%) Estimates CI (95%) Estimates CI (95%) Estimates CI (95%) Estimates CI (95%)
Intercept 0.01 -0.01 – 0.02 -0.06 -0.12 – -0.01 0.02 -0.01 – 0.05 4.05 3.68 – 4.41 4.10 3.81 – 4.39 4.14 3.81 – 4.49 0.01 -0.01 – 0.02 0.27 0.20 – 0.34 -0.10 -0.18 – -0.02 4.05 3.68 – 4.42 4.11 3.81 – 4.40 4.12 3.79 – 4.46 0.01 -0.02 – 0.04 0.27 0.19 – 0.34 -0.08 -0.13 – -0.02 3.59 3.20 – 3.98 3.80 3.48 – 4.12 3.80 3.44 – 4.16
effsize -0.12 -0.15 – -0.10 -0.09 -0.24 – 0.06 -0.06 -0.19 – 0.07 -0.05 -0.17 – 0.07 -0.12 -0.15 – -0.10 -0.09 -0.24 – 0.05 -0.06 -0.19 – 0.07 -0.05 -0.17 – 0.07
effsize_u3 -0.68 -0.77 – -0.58 -0.68 -0.78 – -0.59
effsize_abs 0.07 -0.05 – 0.18 0.19 0.13 – 0.26
typehalfeye_xaxis -0.01 -0.05 – 0.03 0.00 -0.05 – 0.06 0.02 -0.03 – 0.06 0.64 0.42 – 0.87 0.39 0.18 – 0.59 0.51 0.32 – 0.70
typehalfeye_yaxis 0.00 -0.04 – 0.05 0.04 -0.02 – 0.10 -0.01 -0.06 – 0.03 0.97 0.74 – 1.19 0.60 0.40 – 0.80 0.58 0.39 – 0.78
typeraincloud_yaxis 0.00 -0.04 – 0.05 -0.02 -0.08 – 0.04 0.00 -0.05 – 0.05 0.24 0.02 – 0.46 0.24 0.04 – 0.44 0.23 0.04 – 0.42
Random Effects
σ2 0.03 0.04 0.03 1.72 1.32 1.17 0.03 0.02 0.04 1.72 1.32 1.17 0.03 0.02 0.02 1.58 1.27 1.11
τ00 0.00 session 0.01 session 0.00 session 1.31 session 0.87 session 1.14 session 0.00 session 0.01 session 0.01 session 1.32 session 0.87 session 1.14 session 0.00 session 0.01 session 0.00 session 1.32 session 0.87 session 1.15 session
ICC 0.02 0.17 0.11 0.43 0.40 0.49 0.02 0.29 0.18 0.43 0.40 0.50 0.02 0.28 0.12 0.45 0.41 0.51
N 40 session 18 session 31 session 40 session 40 session 40 session 40 session 18 session 18 session 40 session 40 session 40 session 40 session 18 session 31 session 40 session 40 session 40 session
Observations 480 216 372 960 960 960 480 216 216 960 960 960 480 216 372 960 960 960
Marginal R2 / Conditional R2 0.000 / 0.016 0.000 / 0.150 0.000 / 0.104 0.000 / 0.413 0.000 / 0.376 0.000 / 0.476 0.152 / 0.171 0.410 / 0.566 0.006 / 0.159 0.001 / 0.414 0.001 / 0.377 0.000 / 0.476 0.157 / 0.176 0.423 / 0.573 0.083 / 0.188 0.050 / 0.463 0.025 / 0.401 0.026 / 0.501

Sensitivity

Graphical Overview

Code 
ggplot(study1_w %>% 
           select(sensi_ordinal, type) %>% 
           na.omit(), aes(sensi_ordinal, 
                          color = sensi_ordinal,
                          fill = sensi_ordinal)) +
    facet_wrap(~ type) +
    geom_bar() +
    theme_modern_rc() +
    theme(strip.text = element_text(color = "white")) +
    ggtitle("Sensitivity", "all participants")

Code 
ggplot(study1_w %>% 
           select(sensi_ordinal, type, session) %>% 
           na.omit() %>% 
           filter(!session %in% ov_misconceptualizers & 
                      !session %in% u3_misconceptualizers), aes(sensi_ordinal, 
                          color = sensi_ordinal,
                          fill = sensi_ordinal)) +
    facet_wrap(~ type) +
    geom_bar() +
    theme_modern_rc() +
    theme(strip.text = element_text(color = "white")) +
    ggtitle("Sensitivity", "without missconceptualizers")

Code 
ggplot(study1_w %>% 
           select(sensi_correct, type, session) %>%
           dplyr::filter(!is.na(sensi_correct)),
       aes(sensi_correct, 
           color = sensi_correct,
           fill = sensi_correct)) +
    facet_wrap(~ type) +
    geom_bar() +
    theme_modern_rc() +
    theme(strip.text = element_text(color = "white"),
          axis.text.x = element_text(angle = 45, hjust = 1)) +
    labs(color = "", fill = "") +
    ggtitle("Binary Sensitivity", "without wrong decisions")

Code 
ggplot(study1_w %>% 
           select(sensi_binary_filtered, type, session),
       aes(sensi_binary_filtered, 
           color = as.factor(sensi_binary_filtered),
           fill = as.factor(sensi_binary_filtered))) +
    facet_wrap(~ type) +
    geom_bar() +
    theme_modern_rc() +
    theme(strip.text = element_text(color = "white")) +
    labs(color = "", fill = "") +
    ggtitle("Binary Sensitivity", "without wrong decisions (0=equal, 1=right direction)")

Logistic Regressions With and Without Visualization Type

Fitting a series of logistic regressions with non-informative priors

We generally compare

  1. a model (mod0) with intercept only
  2. a model (mod1) with intercept + plotted effect size (control variable)
  3. a model (mod2) with intercept + plotted effect size + visualization type
Code 
logreg_mod0 <- brm(
    sensi_binary_filtered ~ +(1 | session),
    family = bernoulli(link = "logit"),
    data = study1_w,
    save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4
    
)

logreg_mod1 <-
    brm(
        sensi_binary_filtered ~ effsize_abs + (1 | session),
        family = bernoulli(link = "logit"),
        data = study1_w,
        save_pars = save_pars(all = TRUE),
        silent = 2,
        refresh = 0,
        cores = 4
        
    )

logreg_mod2 <-
    brm(
        sensi_binary_filtered ~ effsize_abs + type + (1 | session),
        family = bernoulli(link = "logit"),
        data = study1_w,
        save_pars = save_pars(all = TRUE),
        silent = 2,
        refresh = 0,
        cores = 4
        
    )
Code 
bayes_factor(logreg_mod1, logreg_mod0)
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 6
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Estimated Bayes factor in favor of logreg_mod1 over logreg_mod0: 433078154887206557637255626752.00000
Code 
bayes_factor(logreg_mod2, logreg_mod1)
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 6
Iteration: 7
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 6
Iteration: 7
Estimated Bayes factor in favor of logreg_mod2 over logreg_mod1: 16.62384
Code 
sjPlot::tab_model(logreg_mod0, logreg_mod1, logreg_mod2, show.icc = TRUE)
  sensi_binary_filtered sensi_binary_filtered sensi_binary_filtered
Predictors Odds Ratios CI (95%) Odds Ratios CI (95%) Odds Ratios CI (95%)
Intercept 3.15 1.61 – 6.78 0.10 0.03 – 0.35 0.08 0.02 – 0.30
effsize_abs 2849.05 520.66 – 21632.60 3404.60 578.59 – 27064.16
typehalfeye_xaxis 1.91 0.75 – 5.03
typehalfeye_yaxis 1.84 0.75 – 4.72
typeraincloud_yaxis 0.76 0.30 – 1.93
Random Effects
σ2 3.29 3.29 3.29
τ00 3.95 session 10.34 session 11.03 session
ICC 0.55 0.76 0.77
N 40 session 40 session 40 session
Observations 453 453 453
Marginal R2 / Conditional R2 0.000 / 0.319 0.304 / 0.599 0.310 / 0.605
Code 
pp_check(logreg_mod2) +
    theme_modern_rc() +
    scale_color_manual(values=viridis(2, begin = .3))

Efficiency

Visualisation

Raw Data

Code 
ggplot(study1_w_timestamp, aes(as.factor(plotNrWithin), effic)) +
    geom_boxplot(alpha = .2, color = "lightgrey") +
    geom_sina(alpha = .5) +
    coord_cartesian(ylim = c(0,100000)) + 
    facet_wrap(~type) +
    theme_modern_rc() +
    labs(title ="Dwell Times Until First Decision",
          subtitle = "Per Plot Type and Plot Repetition") +
    theme(strip.text = element_text(color = "white"))

5% Percent Truncated

Code 
ggplot(study1_w_timestamp, aes(as.factor(plotNrWithin), effic_05righttrunc)) +
    geom_boxplot(alpha = .2, color = "lightgrey") +
    geom_sina(alpha = .5) +
    coord_cartesian(ylim = c(0,85000)) + 
    facet_wrap(~type) +
    theme_modern_rc() +
    labs(title ="5% Truncated Dwell Times Until First Decision",
          subtitle = "Per Plot Type and Plot Repetition") +
    theme(strip.text = element_text(color = "white"))

10% Percent Truncated

Code 
ggplot(study1_w_timestamp, aes(as.factor(plotNrWithin), effic_10righttrunc)) +
    geom_boxplot(alpha = .2, color = "lightgrey") +
    geom_sina(alpha = .5) +
    coord_cartesian(ylim = c(0,85000)) + 
    facet_wrap(~type) +
    theme_modern_rc() +
    labs(title ="10% Truncated Dwell Times Until First Decision",
          subtitle = "Per Plot Type and Plot Repetition") +
    theme(strip.text = element_text(color = "white"))

log() Transformed

Code 
ggplot(study1_w_timestamp, 
       aes(as.factor(plotNrWithin), 
           log(effic_05righttrunc))) +
    geom_boxplot(alpha = .2, color = "lightgrey") +
    geom_sina(alpha = .5) +
    facet_wrap(~type) +
    theme_modern_rc() +
    labs(title ="log Transformed Dwell Times Until First Decision",
          subtitle = "Per Plot Type and Plot Repetition") +
    theme(strip.text = element_text(color = "white"))

Modeling With {brms}

We generally compare

  1. a model (mod0) with intercept only
  2. a model (mod1) with intercept + plotted effect size (control variable)
  3. a model (mod2) with intercept + plotted effect size + visualization type

Efficiency for First Plot

Code 
study1_w_timestamp_effsize <- study1_w_timestamp %>% 
    full_join(study1_w %>% select(session, effsize), by = "session")

plot01_mod0 <-
    brm(log_effic_05righttrunc ~ 1 + (1 | session),
        data = study1_w_timestamp_effsize %>%
            filter(plotNrWithin == 1),
        save_pars = save_pars(all = TRUE),
        silent = 2,
        refresh = 0,
        cores = 4,
        iter = 6000)

pp_check(plot01_mod0) +
    theme_modern_rc() +
    scale_color_manual(values=viridis(2, begin = .3))

Code 
plot01_mod1 <-
    brm(log_effic_05righttrunc~ 1 + effsize + (1 | session),
        data = study1_w_timestamp_effsize %>%
            filter(plotNrWithin == 1),
        save_pars = save_pars(all = TRUE),
        silent = 2,
        refresh = 0,
        cores = 4,
        iter = 6000)

pp_check(plot01_mod1) +
    theme_modern_rc() +
    scale_color_manual(values=viridis(2, begin = .3))

Code 
plot01_mod2 <-
    brm(log_effic_05righttrunc ~ 1 + effsize + type + (1 | session),
        data = study1_w_timestamp_effsize %>%
            filter(plotNrWithin == 1),
        save_pars = save_pars(all = TRUE),
        silent = 2,
        refresh = 0,
        cores = 4,
        iter = 6000)

pp_check(plot01_mod2) +
    theme_modern_rc() +
    scale_color_manual(values=viridis(2, begin = .3))

Code 
sjPlot::tab_model(plot01_mod0, plot01_mod1, plot01_mod2)
bayes_factor(plot01_mod1, plot01_mod0)
bayes_factor(plot01_mod2, plot01_mod1)

Efficiency for Last Three Plots

Code 
plot0306_mod0 <-
    brm(log_effic_05righttrunc ~ 1 + plotNrWithin_factor + (1 | session),
        data = study1_w_timestamp_effsize %>%
            filter(plotNrWithin >= 4),
        save_pars = save_pars(all = TRUE),
        silent = 2,
        refresh = 0,
        cores = 4,
        iter = 6000)

pp_check(plot0306_mod0) +
    theme_modern_rc() +
    scale_color_manual(values=viridis(2, begin = .3))

Code 
plot0306_mod1 <-
    brm(log_effic_05righttrunc ~ 1 + plotNrWithin_factor + effsize +
            (1 | session),
        data = study1_w_timestamp_effsize %>%
            filter(plotNrWithin >= 4),
        save_pars = save_pars(all = TRUE),
        silent = 2,
        refresh = 0,
        cores = 4)

pp_check(plot0306_mod1) +
    theme_modern_rc() +
    scale_color_manual(values=viridis(2, begin = .3))

Code 
plot0306_mod2 <-
    brm(log_effic_05righttrunc ~ 1 + plotNrWithin_factor + effsize +
            type + (1 | session),
        data = study1_w_timestamp_effsize %>%
            filter(plotNrWithin >= 4),
        save_pars = save_pars(all = TRUE),
        silent = 2,
        refresh = 0,
        cores = 4)

pp_check(plot0306_mod2) +
    theme_modern_rc() +
    scale_color_manual(values=viridis(2, begin = .3))

Code 
sjPlot::tab_model(plot0306_mod0, plot0306_mod1, plot0306_mod2)
  log_effic_05righttrunc log_effic_05righttrunc log_effic_05righttrunc
Predictors Estimates CI (95%) Estimates CI (95%) Estimates CI (95%)
Intercept 9.47 9.35 – 9.61 9.48 9.34 – 9.62 9.58 9.46 – 9.74
plotNrWithin_factor:
plotNrWithin_factor5		 -0.01 -0.03 – 0.02 -0.01 -0.03 – 0.01 -0.01 -0.03 – 0.01
plotNrWithin_factor:
plotNrWithin_factor6		 -0.19 -0.21 – -0.17 -0.19 -0.21 – -0.17 -0.19 -0.21 – -0.17
effsize 0.00 -0.02 – 0.02 0.00 -0.02 – 0.02
typehalfeye_xaxis -0.13 -0.16 – -0.11
typehalfeye_yaxis -0.21 -0.23 – -0.18
typeraincloud_yaxis -0.06 -0.09 – -0.04
Random Effects
σ2 0.24 0.24 0.24
τ00 0.17 session 0.17 session 0.17 session
ICC 0.41 0.41 0.42
N 40 session 40 session 40 session
Observations 10944 10944 10944
Marginal R2 / Conditional R2 0.019 / 0.406 0.019 / 0.406 0.034 / 0.421
Code 
bayes_factor(plot0306_mod1, plot0306_mod0)
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 6
Iteration: 7
Iteration: 8
Iteration: 9
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 6
Estimated Bayes factor in favor of plot0306_mod1 over plot0306_mod0: 0.02028
Code 
bayes_factor(plot0306_mod2, plot0306_mod1)
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 6
Iteration: 7
Iteration: 8
Iteration: 1
Iteration: 2
Iteration: 3
Iteration: 4
Iteration: 5
Iteration: 6
Iteration: 7
Iteration: 8
Estimated Bayes factor in favor of plot0306_mod2 over plot0306_mod1: 20740578342311886672249858154138483520979767321541214208.00000

Research Question 2

Contrast Effects

Graphical Overview

Code 
# preparing multilevel model with brms for graphical overview

# rating ov
mod_plot_diffov <- brm (
    diff_ov ~ (1 | type),
    data = study1_w %>% 
        filter(rating_ov_missconcept == F),
    control = list(adapt_delta = .999),
    cores = 4,
    iter = 10000
    
)


plot_diffov <- mod_plot_diffov %>%
  spread_draws(b_Intercept, r_type[type,]) %>%
  mutate(type_mean = b_Intercept + r_type) %>%
  ggplot(aes(y = type, x = type_mean
             )) +
    stat_halfeye() + 
    theme_ipsum_rc()+
    theme(axis.title.x = element_blank(),
          axis.text.y = element_text(hjust = 0)) +
    ggtitle('Accuracy in Overlap Metric')
Code 
plot_diffov

Code 
ggsave("4_study1/plot_diffov.png", 
    plot_diffov,
    width = 25*.55,
    height = 16*.55)
Code 
# difficulty
mod_plot_diffi <- brm (
    scale(diffi) ~ (1 | type),
    data = study1_w,
    control = list(adapt_delta = .999),
    cores = 4,
    iter = 10000
    
)

plot_diffi <- mod_plot_diffi %>%
  spread_draws(b_Intercept, r_type[type,]) %>%
  mutate(type_mean = b_Intercept + r_type) %>%
  ggplot(aes(y = type, x = type_mean
             )) +
    stat_halfeye() +
    theme_ipsum_rc() +
    theme(axis.title.x = element_blank(),
          axis.text.y = element_text(hjust = 0)) +
    ggtitle('Perceived Task Difficulty')
Code 
# informativity
mod_plot_infor <- brm (
    scale(infor) ~ (1 | type),
    data = study1_w,
    control = list(adapt_delta = .999),
    cores = 4,
    iter = 10000
    
)

plot_infor <- mod_plot_infor %>%
  spread_draws(b_Intercept, r_type[type,]) %>%
  mutate(type_mean = b_Intercept + r_type) %>%
  ggplot(aes(y = type, x = type_mean
             )) +
  stat_halfeye() +
    theme_ipsum_rc() +
    theme(axis.title.x = element_blank(),
          axis.text.y = element_blank()) +
    ggtitle('Perceived Informativity')
Code 
# value 
mod_plot_value <- brm (
    scale(value) ~ (1 | type),
    data = study1_w,
    control = list(adapt_delta = .999),
    cores = 4,
    iter = 10000
    
)

plot_value <- mod_plot_value %>%
  spread_draws(b_Intercept, r_type[type,]) %>%
  mutate(type_mean = b_Intercept + r_type) %>%
  ggplot(aes(y = type, x = type_mean 
             )) +
  stat_halfeye() +
    theme_ipsum_rc() +
    theme(axis.title.x = element_blank(),
          axis.text.y = element_text(hjust = 0)) +
    ggtitle('Perceived Value')
Code 
# efficiency for the first plot

mod_plot_efficiency1 <-
    brm(
        scale(effic) ~ (1 | type),
        data = study1_w_timestamp_effsize %>%
            filter(plotNrWithin == 1),
        control = list(adapt_delta = .999),
        cores = 4
        
    )
 

plot_efficiency1 <- mod_plot_efficiency1 %>%
  spread_draws(b_Intercept, r_type[type,]) %>%
  mutate(type_mean = b_Intercept + r_type) %>%
  ggplot(aes(y = type, x = type_mean 
             )) +
  stat_halfeye() +
    theme_ipsum_rc() +
    theme(axis.title.x = element_blank(),
          axis.text.y = element_blank(), 
          axis.title.y = element_blank()) +
    ggtitle('Efficiency for the First Plot')
Code 
plot_contrasteffects <- plot_diffi + plot_infor + plot_value + plot_efficiency1 + 
    plot_layout(ncol=2)

plot_contrasteffects

Code 
ggsave("4_study1/plot_contrasteffects.png", 
    plot_contrasteffects,
    width = 25*.55,
    height = 16*.55)

Model Contrast Effects with {brms}

Code 
# create dummy variables to compare visualization types for those measures that showed evidence for difference (accuracy overlap, perceived task difficulty, perceived informativity, perceived value, sensitivity, efficiency)


## Gardner Altman Plot vs. Halfeye xaxis
gardneraltman_vs_halfeye_x <- study1_w %>%
    group_by(session) %>%
    mutate(dummy_gardneraltman_halfeye_x = 
               case_when(type == "gardneraltman_xaxis" ~ 0, TRUE ~ 1)) %>%
    filter(type == "gardneraltman_xaxis" | type == "halfeye_xaxis") %>%
    ungroup()

gardneraltman_vs_halfeye_x_effic <- study1_w_timestamp %>%
    group_by(session) %>%
    mutate(dummy_gardneraltman_halfeye_x = 
               case_when(type == "gardneraltman_xaxis" ~ 0, TRUE ~ 1)) %>%
    filter(type == "gardneraltman_xaxis" | type == "halfeye_xaxis") %>%
    ungroup() %>% 
    full_join(study1_w %>% select(session, effsize), by = "session")
Code 
mod_diffov_gardneraltman_halfeye_x <- 
    brm(diff_ov ~ dummy_gardneraltman_halfeye_x +  effsize_abs + (1|session), 
                          data = gardneraltman_vs_halfeye_x%>% 
                              filter(rating_ov_missconcept == F),
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4,
    iter = 10000)
Code 
mod_diffi_gardneraltman_halfeye_x <- 
    brm(scale(diffi) ~ dummy_gardneraltman_halfeye_x + effsize 
        + (1|session), 
                          data = gardneraltman_vs_halfeye_x,
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4,
    iter = 10000)
Code 
mod_infor_gardneraltman_halfeye_x <- 
    brm(scale(infor) ~ dummy_gardneraltman_halfeye_x + effsize
        + (1|session), 
                          data = gardneraltman_vs_halfeye_x,
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4,
    iter = 10000)

mod_value_gardneraltman_halfeye_x <- 
    brm(scale(value) ~ dummy_gardneraltman_halfeye_x + effsize 
        + (1|session), 
                          data = gardneraltman_vs_halfeye_x,
                          save_pars = save_pars(all = TRUE))
Code 
mod_sensi_gardneraltman_halfeye_x <-
    brm(
        sensi_binary_filtered ~ dummy_gardneraltman_halfeye_x + effsize_abs + (1 | session),
        family = bernoulli(link = "logit"),
        data = gardneraltman_vs_halfeye_x,
        save_pars = save_pars(all = TRUE),
        silent = 2,
        refresh = 0,
        cores = 4
    )
Code 
mod_effic01_gardneraltman_halfeye_x <- 
    brm(scale(log_effic_05righttrunc) ~ dummy_gardneraltman_halfeye_x + 
            effsize + (1|session),
    data = gardneraltman_vs_halfeye_x_effic %>%  
    filter(plotNrWithin == 1),
    save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4,
    iter = 10000)

mod_effic0306_gardneraltman_halfeye_x <- 
    brm(scale(log_effic_05righttrunc) ~ dummy_gardneraltman_halfeye_x +
            effsize + (1|session),
    data = gardneraltman_vs_halfeye_x_effic %>% 
        filter(plotNrWithin >= 4),
    save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4,
    iter = 10000)
Code 
## Gardner Altman Plot vs. Halfeye yaxis
gardneraltman_vs_halfeye_y <- study1_w %>%
    group_by(session) %>%
    mutate(dummy_gardneraltman_halfeye_y = 
               case_when(type == "gardneraltman_xaxis" ~ 0, TRUE ~ 1)) %>%
    filter(type == "gardneraltman_xaxis" | type == "halfeye_yaxis") %>%
    ungroup()


gardneraltman_vs_halfeye_y_effic <- study1_w_timestamp %>%
    group_by(session) %>%
    mutate(dummy_gardneraltman_halfeye_y = 
               case_when(type == "gardneraltman_xaxis" ~ 0, TRUE ~ 1)) %>%
    filter(type == "gardneraltman_xaxis" | type == "halfeye_yaxis") %>%
    ungroup()  %>% 
    full_join(study1_w %>% select(session, effsize), by = "session")
Code 
mod_diffov_gardneraltman_halfeye_y <- 
    brm(diff_ov ~ dummy_gardneraltman_halfeye_y + effsize_abs + (1|session), 
                          data = gardneraltman_vs_halfeye_y%>% 
                              filter(rating_ov_missconcept == F),
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)
Code 
mod_diffi_gardneraltman_halfeye_y <- 
    brm(scale(diffi) ~ dummy_gardneraltman_halfeye_y + effsize 
        + (1|session), 
                          data = gardneraltman_vs_halfeye_y,
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)
Code 
mod_infor_gardneraltman_halfeye_y <- 
    brm(scale(infor) ~ dummy_gardneraltman_halfeye_y + effsize 
        + (1|session), 
                          data = gardneraltman_vs_halfeye_y,
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)

mod_value_gardneraltman_halfeye_y <- 
    brm(scale(value) ~ dummy_gardneraltman_halfeye_y + effsize 
        + (1|session), 
                          data = gardneraltman_vs_halfeye_y,
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)
Code 
mod_sensi_gardneraltman_halfeye_y <-
    brm(
        sensi_binary_filtered ~ dummy_gardneraltman_halfeye_y + effsize_abs + (1 | session),
        family = bernoulli(link = "logit"),
        data = gardneraltman_vs_halfeye_y,
        save_pars = save_pars(all = TRUE),
        silent = 2,
        refresh = 0,
        cores = 4
    )
Code 
mod_effic01_gardneraltman_halfeye_y <- 
    brm(scale(log_effic_05righttrunc) ~ dummy_gardneraltman_halfeye_y +
            effsize + (1|session),
    data = gardneraltman_vs_halfeye_y_effic %>%  
    filter(plotNrWithin == 1),
    save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)

mod_effic0306_gardneraltman_halfeye_y <- 
    brm(scale(log_effic_05righttrunc) ~ dummy_gardneraltman_halfeye_y + 
            effsize + (1|session),
    data = gardneraltman_vs_halfeye_y_effic %>% 
        filter(plotNrWithin >= 4),
    save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4,
    iter = 10000)
Code 
## Raincloud Plot vs. Halfeye x axis
raincloud_vs_halfeye_x <- study1_w %>%
    group_by(session) %>%
    mutate(dummy_raincloud_halfeye_x = 
               case_when(type == "raincloud_yaxis" ~ 0, TRUE ~ 1)) %>%
    filter(type == "halfeye_xaxis" | type == "raincloud_yaxis") %>%
    ungroup()

raincloud_vs_halfeye_x_effic <- study1_w_timestamp %>%
    group_by(session) %>%
    mutate(dummy_raincloud_halfeye_x = 
               case_when(type == "raincloud_yaxis" ~ 0, TRUE ~ 1)) %>%
    filter(type == "raincloud_yaxis" | type == "halfeye_xaxis") %>%
    ungroup() %>% 
    full_join(study1_w %>% select(session, effsize), by = "session")
Code 
mod_diffov_raincloud_halfeye_x <- 
    brm(diff_ov ~ dummy_raincloud_halfeye_x + effsize_abs + (1|session), 
                          data = raincloud_vs_halfeye_x %>% 
                              filter(rating_ov_missconcept == F),
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)
Code 
mod_diffi_raincloud_halfeye_x <- 
    brm(scale(diffi) ~ dummy_raincloud_halfeye_x + 
            effsize + (1|session), 
                          data = raincloud_vs_halfeye_x,
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)
Code 
mod_infor_raincloud_halfeye_x <- 
    brm(scale(infor) ~ dummy_raincloud_halfeye_x +
        effsize + (1|session), 
                          data = raincloud_vs_halfeye_x,
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)

mod_value_raincloud_halfeye_x <- 
    brm(scale(value) ~ dummy_raincloud_halfeye_x + 
            effsize + (1|session), 
                          data = raincloud_vs_halfeye_x,
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)
Code 
mod_sensi_raincloud_halfeye_x <-
    brm(
        sensi_binary_filtered ~ dummy_raincloud_halfeye_x + effsize_abs + (1 | session),
        family = bernoulli(link = "logit"),
        data = raincloud_vs_halfeye_x,
        save_pars = save_pars(all = TRUE),
        silent = 2,
        refresh = 0,
        cores = 4
    )
Code 
mod_effic01_raincloud_halfeye_x <- 
    brm(scale(log_effic_05righttrunc) ~ dummy_raincloud_halfeye_x + 
            effsize + (1|session),
    data = raincloud_vs_halfeye_x_effic %>%  
    filter(plotNrWithin == 1),
    save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4,
    iter = 10000)

mod_effic0306_raincloud_halfeye_x <- 
    brm(scale(log_effic_05righttrunc) ~ dummy_raincloud_halfeye_x +
            effsize + (1|session),
    data = raincloud_vs_halfeye_x_effic %>% 
        filter(plotNrWithin >= 4),
    save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4,
    iter = 10000)
Code 
##  Raincloud Plot vs.Halfeye yaxis
raincloud_vs_halfeye_y <- study1_w %>%
    group_by(session) %>%
    mutate(dummy_raincloud_halfeye_y = 
               case_when(type == "raincloud_yaxis" ~ 0, TRUE ~ 1)) %>%
    filter(type == "halfeye_yaxis" | type == "raincloud_yaxis") %>%
    ungroup()

raincloud_vs_halfeye_y_effic <- study1_w_timestamp %>%
    group_by(session) %>%
    mutate(dummy_raincloud_halfeye_y = 
               case_when(type == "raincloud_yaxis" ~ 0, TRUE ~ 1)) %>%
    filter(type == "raincloud_yaxis" | type == "halfeye_yaxis") %>%
    ungroup() %>% 
    full_join(study1_w %>% select(session, effsize), by = "session")
Code 
mod_diffov_raincloud_halfeye_y <- 
    brm(diff_ov ~ dummy_raincloud_halfeye_y + effsize_abs + (1|session), 
                          data = raincloud_vs_halfeye_y %>% 
                              filter(rating_ov_missconcept == F),
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)
Code 
mod_diffi_raincloud_halfeye_y <- 
    brm(scale(diffi) ~ dummy_raincloud_halfeye_y + 
            effsize + (1|session), 
                          data = raincloud_vs_halfeye_y,
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)
Code 
mod_infor_raincloud_halfeye_y <- 
    brm(scale(infor) ~ dummy_raincloud_halfeye_y + 
            effsize + (1|session), 
                          data = raincloud_vs_halfeye_y,
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)

mod_value_raincloud_halfeye_y <- 
    brm(scale(value) ~ dummy_raincloud_halfeye_y + 
            effsize + (1|session), 
                          data = raincloud_vs_halfeye_y,
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)
Code 
mod_sensi_raincloud_halfeye_y <-
    brm(
        sensi_binary_filtered ~ dummy_raincloud_halfeye_y + effsize_abs + (1 | session),
        family = bernoulli(link = "logit"),
        data = raincloud_vs_halfeye_y,
        save_pars = save_pars(all = TRUE),
        silent = 2,
        refresh = 0,
        cores = 4
    )
Code 
mod_effic01_raincloud_halfeye_y <- 
    brm(scale(log_effic_05righttrunc) ~ dummy_raincloud_halfeye_y +
            effsize + (1|session),
    data = raincloud_vs_halfeye_y_effic %>%  
    filter(plotNrWithin == 1),
    save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4,
    iter = 10000)

mod_effic0306_raincloud_halfeye_y <- 
    brm(scale(log_effic_05righttrunc) ~ dummy_raincloud_halfeye_y +
            effsize + (1|session),
    data = raincloud_vs_halfeye_y_effic %>% 
        filter(plotNrWithin >= 4),
    save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4,
    iter = 10000)
Code 
sjPlot::tab_model(
        mod_diffov_gardneraltman_halfeye_x, 
        mod_diffi_gardneraltman_halfeye_x, 
        mod_infor_gardneraltman_halfeye_x, mod_value_gardneraltman_halfeye_x,
        mod_sensi_gardneraltman_halfeye_x,
        mod_effic01_gardneraltman_halfeye_x, mod_effic0306_gardneraltman_halfeye_x,
        mod_diffov_gardneraltman_halfeye_y, 
        mod_diffi_gardneraltman_halfeye_y, mod_infor_gardneraltman_halfeye_y, 
        mod_value_gardneraltman_halfeye_y, mod_sensi_gardneraltman_halfeye_y,
        mod_effic01_gardneraltman_halfeye_y, mod_effic0306_gardneraltman_halfeye_y,
        mod_diffov_raincloud_halfeye_x, mod_diffi_raincloud_halfeye_x, 
        mod_infor_raincloud_halfeye_x, mod_value_raincloud_halfeye_x,
        mod_sensi_raincloud_halfeye_x,
        mod_effic01_raincloud_halfeye_x, mod_effic0306_raincloud_halfeye_x,
        mod_diffov_raincloud_halfeye_y, 
        mod_diffi_raincloud_halfeye_y, mod_infor_raincloud_halfeye_y, 
        mod_value_raincloud_halfeye_y, mod_sensi_raincloud_halfeye_y,
        mod_effic01_raincloud_halfeye_y, mod_effic0306_raincloud_halfeye_y)
  diff_ov scale(diffi) scale(infor) scale(value) sensi_binary_filtered scale(log_effic_05righttrunc) scale(log_effic_05righttrunc) diff_ov scale(diffi) scale(infor) scale(value) sensi_binary_filtered scale(log_effic_05righttrunc) scale(log_effic_05righttrunc) diff_ov scale(diffi) scale(infor) scale(value) sensi_binary_filtered scale(log_effic_05righttrunc) scale(log_effic_05righttrunc) diff_ov scale(diffi) scale(infor) scale(value) sensi_binary_filtered scale(log_effic_05righttrunc) scale(log_effic_05righttrunc)
Predictors Estimates CI (95%) Estimates CI (95%) Estimates CI (95%) Estimates CI (95%) Odds Ratios CI (95%) Estimates CI (95%) Estimates CI (95%) Estimates CI (95%) Estimates CI (95%) Estimates CI (95%) Estimates CI (95%) Odds Ratios CI (95%) Estimates CI (95%) Estimates CI (95%) Estimates CI (95%) Estimates CI (95%) Estimates CI (95%) Estimates CI (95%) Odds Ratios CI (95%) Estimates CI (95%) Estimates CI (95%) Estimates CI (95%) Estimates CI (95%) Estimates CI (95%) Estimates CI (95%) Odds Ratios CI (95%) Estimates CI (95%) Estimates CI (95%)
Intercept -0.11 -0.17 – -0.06 -0.19 -0.44 – 0.07 -0.13 -0.37 – 0.12 -0.17 -0.44 – 0.08 0.08 0.01 – 0.41 0.33 0.08 – 0.59 0.10 -0.11 – 0.31 -0.08 -0.16 – -0.01 -0.27 -0.50 – -0.03 -0.20 -0.44 – 0.03 -0.20 -0.46 – 0.05 0.04 0.00 – 0.25 0.39 0.14 – 0.68 0.18 -0.03 – 0.37 -0.08 -0.13 – -0.03 -0.13 -0.36 – 0.12 -0.05 -0.28 – 0.17 -0.09 -0.35 – 0.16 0.08 0.01 – 0.32 -0.05 -0.34 – 0.25 0.07 -0.17 – 0.30 -0.04 -0.11 – 0.03 -0.22 -0.46 – 0.01 -0.12 -0.34 – 0.10 -0.12 -0.37 – 0.12 0.05 0.01 – 0.22 0.05 -0.25 – 0.34 0.14 -0.09 – 0.38
dummy_gardneraltman_halfeye_x 0.02 -0.02 – 0.06 0.37 0.25 – 0.49 0.26 0.14 – 0.38 0.35 0.23 – 0.46 1.73 0.63 – 5.04 -0.69 -0.75 – -0.64 -0.20 -0.24 – -0.16
effsize_abs 0.27 0.18 – 0.35 3800.60 239.41 – 119388.20 0.20 0.09 – 0.31 22342.40 876.18 – 1634719.84 0.19 0.11 – 0.27 1407.58 134.05 – 31213.09 0.12 0.02 – 0.24 3670.15 320.89 – 82033.96
effsize -0.04 -0.15 – 0.06 -0.02 -0.14 – 0.09 -0.05 -0.15 – 0.05 -0.00 -0.05 – 0.05 -0.00 -0.04 – 0.04 -0.04 -0.15 – 0.08 -0.03 -0.15 – 0.09 -0.02 -0.13 – 0.10 -0.00 -0.04 – 0.04 0.00 -0.04 – 0.04 -0.07 -0.19 – 0.05 -0.06 -0.18 – 0.07 -0.05 -0.16 – 0.07 -0.00 -0.05 – 0.05 0.00 -0.03 – 0.03 -0.06 -0.18 – 0.05 -0.06 -0.19 – 0.06 -0.01 -0.13 – 0.10 -0.00 -0.04 – 0.04 0.00 -0.03 – 0.03
dummy_gardneraltman_halfeye_y -0.01 -0.06 – 0.04 0.54 0.42 – 0.66 0.40 0.27 – 0.54 0.39 0.27 – 0.52 1.89 0.69 – 5.62 -0.79 -0.84 – -0.74 -0.32 -0.37 – -0.28
dummy_raincloud_halfeye_x 0.03 -0.02 – 0.06 0.25 0.11 – 0.38 0.10 -0.04 – 0.24 0.19 0.06 – 0.32 2.40 0.92 – 6.38 0.15 0.10 – 0.20 -0.12 -0.16 – -0.08
dummy_raincloud_halfeye_y -0.02 -0.06 – 0.03 0.43 0.31 – 0.56 0.25 0.11 – 0.39 0.24 0.10 – 0.36 2.53 0.97 – 7.35 -0.00 -0.05 – 0.05 -0.23 -0.27 – -0.19
Random Effects
σ2 0.02 0.43 0.46 0.40 3.29 0.35 0.58 0.03 0.46 0.55 0.47 3.29 0.25 0.58 0.02 0.55 0.62 0.50 3.29 0.31 0.54 0.03 0.54 0.60 0.53 3.29 0.26 0.51
τ00 0.00 session 0.59 session 0.57 session 0.63 session 12.36 session 0.60 session 0.44 session 0.01 session 0.51 session 0.45 session 0.54 session 16.16 session 0.70 session 0.42 session 0.00 session 0.48 session 0.41 session 0.53 session 7.44 session 0.78 session 0.49 session 0.00 session 0.46 session 0.42 session 0.50 session 7.89 session 0.86 session 0.52 session
ICC 0.07 0.58 0.55 0.62 0.79 0.63 0.43 0.21 0.52 0.45 0.53 0.83 0.74 0.42 0.04 0.47 0.40 0.52 0.69 0.71 0.48 0.12 0.46 0.41 0.48 0.71 0.77 0.50
N 31 session 40 session 40 session 40 session 40 session 39 session 40 session 31 session 40 session 40 session 40 session 40 session 40 session 40 session 31 session 40 session 40 session 40 session 40 session 39 session 40 session 31 session 40 session 40 session 40 session 40 session 40 session 40 session
Observations 185 480 480 480 223 1824 5472 177 480 480 480 236 1824 5472 195 480 480 480 217 1824 5472 187 480 480 480 230 1824 5472
Marginal R2 / Conditional R2 0.172 / 0.225 0.036 / 0.579 0.019 / 0.543 0.032 / 0.608 0.285 / 0.636 0.118 / 0.654 0.010 / 0.418 0.069 / 0.252 0.074 / 0.541 0.042 / 0.452 0.040 / 0.532 0.341 / 0.682 0.151 / 0.753 0.027 / 0.419 0.103 / 0.142 0.018 / 0.461 0.005 / 0.385 0.011 / 0.509 0.297 / 0.553 0.006 / 0.688 0.004 / 0.461 0.034 / 0.146 0.050 / 0.468 0.019 / 0.408 0.015 / 0.471 0.339 / 0.568 0.000 / 0.744 0.013 / 0.488
Code 
## Gardner Altman Plot vs. Raincloud Plot
gardneraltman_vs_raincloud <- study1_w %>%
    group_by(session) %>%
    mutate(dummy_gardneraltman_raincloud = 
               case_when(type == "gardneraltman_xaxis" ~ 0, TRUE ~ 1)) %>%
    filter(type == "gardneraltman_xaxis" | type == "raincloud_yaxis") %>%
    ungroup()

gardneraltman_vs_raincloud_effic <- study1_w_timestamp %>%
    group_by(session) %>%
    mutate(dummy_gardneraltman_raincloud = 
               case_when(type == "gardneraltman_xaxis" ~ 0, TRUE ~ 1)) %>%
    filter(type == "gardneraltman_xaxis" | type == "raincloud_yaxis") %>%
    ungroup() %>% 
    full_join(study1_w %>% select(session, effsize), by = "session")
Code 
mod_diffov_gardneraltman_raincloud <- 
    brm(diff_ov ~ dummy_gardneraltman_raincloud + effsize_abs + (1|session), 
                          data = gardneraltman_vs_raincloud%>% 
                              filter(rating_ov_missconcept == F),
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)
Code 
mod_diffi_gardneraltman_raincloud <- 
    brm(scale(diffi) ~ dummy_gardneraltman_raincloud + 
            effsize + (1|session), 
                          data = gardneraltman_vs_raincloud,
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)
Code 
mod_infor_gardneraltman_raincloud <- 
    brm(scale(infor) ~ dummy_gardneraltman_raincloud +
            effsize + (1|session), 
        data = gardneraltman_vs_raincloud,
        save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)

mod_value_gardneraltman_raincloud <- 
    brm(scale(value) ~ dummy_gardneraltman_raincloud + 
            effsize + (1|session), 
                          data = gardneraltman_vs_raincloud,
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)
Code 
mod_sensi_gardneraltman_raincloud <-
    brm(
        sensi_binary_filtered ~ dummy_gardneraltman_raincloud + effsize_abs + (1 | session),
        family = bernoulli(link = "logit"),
        data = gardneraltman_vs_raincloud,
        save_pars = save_pars(all = TRUE),
        silent = 2,
        refresh = 0,
        cores = 4
    )
Code 
mod_effic01_gardneraltman_raincloud <- 
    brm(scale(log_effic_05righttrunc) ~ dummy_gardneraltman_raincloud + 
            effsize + (1|session),
    data = gardneraltman_vs_raincloud_effic %>%  
    filter(plotNrWithin == 1),
    save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4,
    iter = 10000)

mod_effic0306_gardneraltman_raincloud <- 
    brm(scale(log_effic_05righttrunc) ~ dummy_gardneraltman_raincloud + 
            effsize + (1|session),
    data = gardneraltman_vs_raincloud_effic %>% 
        filter(plotNrWithin >= 4),
    save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4,
    iter = 10000)
Code 
## Halfeye xaxis vs. Halfeye yaxis

halfeye_x_vs_halfeye_y <- study1_w %>%
    group_by(session) %>%
    mutate(dummy_halfeye_x_halfeye_y = 
               case_when(type == "halfeye_xaxis" ~ 0, TRUE ~ 1)) %>%
    filter(type == "halfeye_xaxis" | type == "halfeye_yaxis") %>%
    ungroup()

halfeye_x_vs_halfeye_y_effic <- study1_w_timestamp %>%
    group_by(session) %>%
    mutate(dummy_halfeye_x_halfeye_y = 
               case_when(type == "halfeye_xaxis" ~ 0, TRUE ~ 1)) %>%
    filter(type == "halfeye_xaxis" | type == "halfeye_yaxis") %>%
    ungroup() %>% 
    full_join(study1_w %>% select(session, effsize), by = "session")
Code 
mod_diffov_halfeye_x_halfeye_y <- 
    brm(diff_ov ~ dummy_halfeye_x_halfeye_y + effsize_abs + (1|session), 
                          data = halfeye_x_vs_halfeye_y%>% 
                              filter(rating_ov_missconcept == F),
                          save_pars = save_pars(all = TRUE),
        
    silent = 2,
    refresh = 0,
    cores = 4,
    iter = 20000)
Code 
mod_diffi_halfeye_x_halfeye_y <- 
    brm(scale(diffi) ~ dummy_halfeye_x_halfeye_y +
            effsize + (1|session), 
                          data = halfeye_x_vs_halfeye_y,
                          iter = 10000,
                          save_pars = save_pars(all = TRUE))
Code 
mod_infor_halfeye_x_halfeye_y <- 
    brm(scale(infor) ~ dummy_halfeye_x_halfeye_y + 
            effsize + (1|session), 
                          data = halfeye_x_vs_halfeye_y,
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4)

mod_value_halfeye_x_halfeye_y <- 
    brm(scale(value) ~ dummy_halfeye_x_halfeye_y + 
            effsize + (1|session), 
                          data = halfeye_x_vs_halfeye_y,
                          save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4,
    iter = 10000)
Code 
mod_sensi_halfeye_x_halfeye_y <-
    brm(
        sensi_binary_filtered ~ dummy_halfeye_x_halfeye_y + effsize_abs + (1 | session),
        family = bernoulli(link = "logit"),
        data = halfeye_x_vs_halfeye_y,
        save_pars = save_pars(all = TRUE),
        silent = 2,
        refresh = 0,
        cores = 4
    )
Code 
mod_effic01_halfeye_x_halfeye_y <- 
    brm(scale(log_effic_05righttrunc) ~ dummy_halfeye_x_halfeye_y + 
            effsize + (1|session),
    data = halfeye_x_vs_halfeye_y_effic %>%  
    filter(plotNrWithin == 1),
    save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    iter = 10000)

mod_effic0306_halfeye_x_halfeye_y <- 
    brm(scale(log_effic_05righttrunc) ~ dummy_halfeye_x_halfeye_y + 
            effsize + (1|session),
    data = halfeye_x_vs_halfeye_y_effic%>% 
        filter(plotNrWithin >= 4),
    save_pars = save_pars(all = TRUE),
    silent = 2,
    refresh = 0,
    cores = 4,
    iter = 10000)
Code 
sjPlot::tab_model(mod_diffov_gardneraltman_raincloud, 
                  mod_diffi_gardneraltman_raincloud,
                  mod_infor_gardneraltman_raincloud, 
                  mod_value_gardneraltman_raincloud,
                  mod_sensi_gardneraltman_raincloud,
                  mod_effic01_gardneraltman_raincloud, 
                  mod_effic0306_gardneraltman_raincloud)
  diff_ov scale(diffi) scale(infor) scale(value) sensi_binary_filtered scale(log_effic_05righttrunc) scale(log_effic_05righttrunc)
Predictors Estimates CI (95%) Estimates CI (95%) Estimates CI (95%) Estimates CI (95%) Odds Ratios CI (95%) Estimates CI (95%) Estimates CI (95%)
Intercept -0.08 -0.14 – -0.01 -0.07 -0.29 – 0.16 -0.08 -0.31 – 0.16 -0.08 -0.33 – 0.16 0.13 0.02 – 0.55 0.40 0.13 – 0.66 0.05 -0.16 – 0.25
dummy_gardneraltman_raincloud -0.00 -0.05 – 0.05 0.14 0.00 – 0.27 0.16 0.01 – 0.30 0.15 0.02 – 0.28 0.83 0.32 – 2.19 -0.77 -0.81 – -0.72 -0.10 -0.14 – -0.06
effsize_abs 0.19 0.09 – 0.29 1255.82 122.43 – 18378.87
effsize -0.09 -0.22 – 0.03 -0.11 -0.24 – 0.01 -0.11 -0.22 – 0.00 -0.00 -0.04 – 0.04 -0.00 -0.04 – 0.04
Random Effects
σ2 0.02 0.59 0.60 0.50 3.29 0.25 0.57
τ00 0.00 session 0.45 session 0.43 session 0.54 session 10.49 session 0.71 session 0.45 session
ICC 0.17 0.43 0.42 0.52 0.76 0.74 0.44
N 31 session 40 session 40 session 40 session 40 session 39 session 40 session
Observations 178 480 480 480 228 1824 5472
Marginal R2 / Conditional R2 0.073 / 0.233 0.009 / 0.420 0.011 / 0.407 0.010 / 0.505 0.278 / 0.586 0.144 / 0.747 0.003 / 0.426
Code 
sjPlot::tab_model(mod_diffov_halfeye_x_halfeye_y, 
                  mod_diffi_halfeye_x_halfeye_y, 
                  mod_infor_halfeye_x_halfeye_y, 
                  mod_value_halfeye_x_halfeye_y,
                  mod_sensi_halfeye_x_halfeye_y,
                  mod_effic01_halfeye_x_halfeye_y,
                  mod_effic0306_halfeye_x_halfeye_y)
  diff_ov scale(diffi) scale(infor) scale(value) sensi_binary_filtered scale(log_effic_05righttrunc) scale(log_effic_05righttrunc)
Predictors Estimates CI (95%) Estimates CI (95%) Estimates CI (95%) Estimates CI (95%) Odds Ratios CI (95%) Estimates CI (95%) Estimates CI (95%)
Intercept -0.06 -0.11 – 0.00 -0.10 -0.34 – 0.15 -0.09 -0.34 – 0.16 -0.03 -0.29 – 0.24 0.02 0.00 – 0.26 0.11 -0.15 – 0.37 0.07 -0.14 – 0.32
dummy_halfeye_x_halfeye_y -0.03 -0.08 – 0.01 0.20 0.08 – 0.33 0.16 0.04 – 0.28 0.05 -0.06 – 0.17 1.09 0.31 – 4.18 -0.14 -0.20 – -0.08 -0.12 -0.16 – -0.09
effsize_abs 0.19 0.09 – 0.28 1329497.06 10080.89 – 2178270902.28
effsize -0.01 -0.12 – 0.10 0.04 -0.07 – 0.15 0.05 -0.05 – 0.16 -0.00 -0.05 – 0.05 -0.00 -0.03 – 0.03
Random Effects
σ2 0.02 0.48 0.47 0.41 3.29 0.37 0.52
τ00 0.00 session 0.56 session 0.58 session 0.65 session 28.17 session 0.73 session 0.52 session
ICC 0.04 0.53 0.55 0.62 0.90 0.66 0.50
N 31 session 40 session 40 session 40 session 40 session 39 session 40 session
Observations 194 480 480 480 225 1824 5472
Marginal R2 / Conditional R2 0.087 / 0.125 0.012 / 0.521 0.008 / 0.539 0.003 / 0.598 0.386 / 0.741 0.005 / 0.626 0.004 / 0.482

References

Arslan, Ruben C., Matthias P. Walther, and Cyril S. Tata. 2020. “Formr: A Study Framework Allowing for Automated Feedback Generation and Complex Longitudinal Experience-Sampling Studies Using R.” Behavior Research Methods 52 (1): 376–87. https://doi.org/10.3758/s13428-019-01236-y.